Method and system for managing a mortgage-backed securities index

ABSTRACT

A system and method for generating and managing a generic mortgage-backed securities index. Bonds are selected for the index on a monthly basis. In order to determine which bonds will be represented in the index during a particular month, a set of calculations is performed during the second business week of the preceding month. For the purpose of selecting bonds for the index, all outstanding mortgage-backed securities are considered. They are first aggregated into pools based on their coupon and original term, and then their total outstanding principals are considered. If the total principal outstanding of any 30-year coupon represents more than a predetermined percentage such as 1.5% of the total, then this 30-year coupon will be included in the Index. Similarly, if the total principal outstanding on any 15-year coupon represents more than a second predetermined percentage such as 0.4% of the total, then this 15-year coupon will be included in the Index. The performance of the Index is measured by its total return. An algorithm for calculating the total return of the generic Index is also provided. The total return of the index partially depends on the relative weight assigned to each particular security included in the index. The present invention provides a method of assigning relative weights in accordance with relative proportions of different individual securities in the index, and covers the frequency of re-weighting.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The invention generally relates to a method and system forgenerating an Index-type benchmark for a mortgage-backed securities(MBS) sector of the securities market.

[0003] 2. Description of the Related Art

[0004] In the stock market, an index is a device that measures changesin the prices of a basket of shares, and represents the changes using asingle Fig. The purpose is to give investors an easy way to see thegeneral direction of shares in the index. The FTSE 100 Index, forexample, is calculated by taking a weighted average of the share pricesof the largest 100 companies on the London Stock Exchange. Launched in1984 with a base Fig. of 1,000, the FTSE is calculated continuouslythroughout the trading day.

[0005] Generally speaking, an index is defined by a pre-determineduniverse of individual issues valued or weighted in proportion to theirsize within the whole universe of issues. The Standard & Poor's 500Index is an example of such an index and is based on the common stocksof the 500 largest corporations which trade on United States exchanges.Illustratively, the weighting for each different security in the S & P500 index is simply the market capitalization of that security expressedas a percentage of the total market capitalization taken across all thesecurities then in the index. Of course, these weights continuallychange as share prices move which, in turn, changes marketcapitalization both of each individual security in the index as well asthat across the entire index. Other indices, such as the Value Lineindex, assign their own, e.g. equal, weightings to each securitytherein.

[0006] Capitalization weighting is the most common approach to equityindices and equity portfolios. Cap-weighted portfolios are easy tomaintain because the rebalancing process takes care of itself. Analgorithm for rebalancing a capitalization weighted stock index isdisclosed, for example, in U.S. Pat. No. 6,061,663 (the '663 patent).The '663 patent teaches a method and system for rebalancing an equityportfolio based on weighting characteristics of individual securities.Similar to other known equity indices, e.g. S&P 500 Index, in the '663patent the weighting characteristic of a particular security is based onthe market capitalization of that security expressed as a percentage ofthe total market capitalization taken across all the securities then inthe index. The computer program disclosed in the '663 patent includesinstructions to classify stocks in the index into several categories bycomparing their capitalization weight to a threshold level.

[0007] Similarly, U.S. Pat. No. 5,819,238 (the '238 patent) discloses amethod for automatically modifying a financial portfolio having apre-defined universe of securities, such as an index fund that tracks agiven capitalization weighted index, through dynamic re-weighting of aposition held in each such security. Specifically, in the disclosedcomputer system, a target weight is associated with each such securityrelative to others in the same portfolio in proportion to a non-constantfunction of current capitalization weights of the securities in theindex. Once these target weights are determined, then, in response toboth the target weight of each such security and an actual weight, as aproportion of the portfolio in which that security was held, a tradewill be generated by the system in order to conform, within a predefinedband, the actual weight to the target weight so as to rebalance theholdings in the portfolio.

[0008] For indices reflecting international securities markets, relativeweights may be calculated based on countries' relative GDPs or imports.

[0009] Indices are currently used in the industry as benchmarks allowinginvestors and portfolio managers to compare performance of one sector ofthe securities market to others. Indices are often used in order tocreate index funds, i.e., funds that purchase securities that mimic orrepresent a specific index, for example the Vanguard 500 Index Fundmimics the composition and, supposedly, performance of the S & P 500stock index.

[0010] Mortgage-Backed Securities are securities backed by mortgageloans, including pass-through securities, modified pass-throughsecurities, mortgage-backed bonds, and mortgage pay-through securities.MBS are created when mortgage loans are pooled and underwritten byeligible issuers. Conmmonly referred to as “pass-through” certificates,these MBS entitle an investor to an undivided interest in the underlyingmortgage loan pool. Thus, an investor receives a pro rata share of theinterest (net of servicing and guaranty fees) and/or principal on theunderlying mortgage loans.

[0011] Several financial institutions have developed indexes formeasuring changes in the MBS markets. For example, Lehman Brothers hasdeveloped an MBS Index (hereinafter “LB MBS Index”) which covers themortgage-backed pass-through securities of GNMA (also known as “GinnieMae”), FNMA (also known as “Fannie Mae”), and FHIMC (also known as“Freddie Mac”). It is formed by grouping the universe of over 600,000individual fixed rate MBS pools into approximately 3,500 genericaggregates. The aggregates included are priced daily using a matrixpricing routine based on trade price quotations by agency, program,coupon, and degree of seasoning. Lehman Brothers also developed aMortgage-Backed Securities Index which is an unmanaged version of the LBMBS index and is composed of all fixed securities mortgage pools byGNMA, FNMA and the FHLMC, including GNMA Graduated Payment Mortgages.

[0012] In order to generate one of the LB MBS indices, a user must firstselect a set of securities that satisfy a number of subjective rules(for example, the total outstanding balance of each generic securitymust be at least $100 million), then price each issue within the indexbased on the provided “matrix pricing,” calculate the returns of eachindividual security within the index and calculate the index return as amarket-weighted average of individual security returns. The weights ofindividual securities are subjectively assigned and are not related tothe proportion of the total outstanding principal on a particularsecurity and total outstanding principal for the selected pool.Additionally, as explained further below, mortgage-backed securities aretraded in “to-be-announced” (TBA) transactions where the purchase priceis settled at some future TBA date. In order to calculate an index'stotal return, TBA settle prices for each security have to be convertedinto same-day-settle prices. According to the LB MBS Index's publishedalgorithm, this process involves complicated calculations which includeadjustments for an unknown future cash flow.

SUMMARY OF THE INVENTION

[0013] The present invention is directed to a method and system forgenerating an MBS Index by objectively selecting securities from allavailable mortgage-backed securities, assigning a relative weight toeach selected security, evaluating the MBS Index by calculating itstotal return and periodically rebalancing the Index. There is a need inthe industry for a system and method for generating an MBS Index, whichwould objectively select mortgage-based securities from the entireuniverse of available securities based on an easy-to-administermathematical algorithm. There is also a need for a simple and objectivesystem and method for calculating total return of the MBS Index based onsame-day-settle price of each included security that would eliminate anyguess work as to the future cash flow.

[0014] It is an object of the present invention to provide a system andmethod for generating an objective benchmark, which will accuratelyreflect the value of the MBS sector of the securities market.

[0015] It is another object of the present invention to provide a systemand method for generating an MBS Index, which will take intoconsideration all outstanding mortgage-backed securities.

[0016] It is a further object of the present invention to provide asystem and method for managing an MBS index, which can be easilyautomatically rebalanced.

[0017] It is still another object of the present invention to provide asystem and method for generating and managing an MBS Index, which willallow portfolio managers to more precisely measure the performance ofthe mortgage-backed securities sector relative to other fixed-incomeinvestments.

[0018] It is still a further object of the present invention to providea system and a method that allow portfolio managers to create mutual orexchange-traded finds, which will purchase, hold and sellmortgage-backed securities mimicking and/or representing the providedMBS Index.

[0019] In accordance with the preferred embodiment of the presentinvention, a system and method for generating and managing an MBS Indexare provided. In order to determine which securities will be representedin the Index during a particular month, the system and method of thepresent invention perform a set of calculations during the secondbusiness week of the preceding month. For the purpose of selectingsecurities for the Index, all outstanding mortgage-backed securities areconsidered. They are preferably aggregated into pools based on theircoupon and original term (e.g. 15 and 30 years). If the total principaloutstanding for any 30-year coupon represents more than 1.5% of thetotal, then this 30-year coupon will be included in the Index.Similarly, if the total principal outstanding on any 15-year couponrepresents more than 0.4% of the total, then this 15-year coupon will beincluded in the Index.

[0020] The performance of the Index is measured by its total return. Thesystem and method of the invention calculate the total return of thegeneric Index in accordance with an algorithm which is provided herein.In the preferred embodiment, the total return of the Index depends on atotal return of each security included in the index weighted accordingto the relative weight assigned to such particular security. The presentinvention provides a method of assigning relative weights, whichrepresent relative proportions of different generic securities in thegeneric MBS Index, and covers the frequency of reweighing. In accordancewith another embodiment of the present invention, the system and methodmay be modified to produce the relative weights of the individualsecurities within Conventional, Government, 30-year, and 15-yearindices.

[0021] The above and other objects, aspects, features and advantages ofthe invention will be more readily apparent from the description of thepreferred embodiments thereof taken in conjunction with the accompanyingdrawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The invention is illustrated by way of the example describedbelow and the Fig.s of the accompanying drawings in which likereferences denote like or corresponding parts, which in no way should beconsidered as a limitation of the invention.

[0023]FIG. 1 is a block diagram of the system 50 of the presentinvention;

[0024]FIG. 2 is a functional diagram of the discrete components andinformation flow within the system for generating and managing an MBSIndex in accordance with the present invention;

[0025]FIG. 3 is the table of The Bond Market Association MBSNotification and Settlement Dates from May 2001 to August 2001, the listwas last updated on Apr. 27, 2001;

[0026]FIG. 4 is a schematic flow chart of the steps to be performed inthe method of the present invention;

[0027]FIG. 5 is a logic flow chart of the processing logic for the indexcomposition determination;

[0028]FIG. 6 is a logic flow chart of the processing logic for therelative weights calculation;

[0029]FIG. 7 is a logic flow chart of the processing logic for thepay-down factor determination;

[0030]FIG. 8 is a logic flow chart of the processing logic for thesame-day-settle price conversion; and

[0031]FIG. 9 is a logic flow chart of the processing logic for thedetermination of total return of the MBS Index.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS AND THE DRAWINGS

[0032] In accordance with the preferred embodiment of the presentinvention, a system and method for generating, evaluating and managingdifferent Mortgage-Backed Securities Indices (hereinafter MBS Indices)are provided. The method of the invention is accomplished by a system,as shown in FIGS. 1 and 2 (described further below), which may beimplemented by a general purpose computer operating in accordance withthe instructions provided by the system. The system 50 is illustrated inthe diagram of FIG. 1 and includes a central processing unit (CPU) 1,memory comprising ROM 4, for permanently storing program instructions,operating parameters, or other data required for system operation, andRAM 5, for the temporary storage and manipulation of data during theoperation of the system 50. The system further includes an input device3 which may be a keyboard, a handwriting recognition device, a voicerecognition device or any other known device for inputting dataincluding any type of hardware or software suitable for inputting datafrom another computer system or the Internet. The above described inputdevices are all designated in the diagram of FIG. 1 with a referencenumber 3. The input device 3 inputs data, operational parameters andcommands to the CPU 1 through an input/output interface 2. Data isoutput from the CPU 1 through another input/output interface 6 to theoutput device 7 which may be a printer, a computer display, a modem, orany other known output device. As described in more detail below, thesystem may comprise a plurality of discrete components which perform thefunctions of selecting mortgage-backed securities to be included in theIndex, assigning relative weight to each selected security, calculatingthe total return of the Index, calculating the level of the Index andother functions in accordance with the present invention. In thepreferred embodiment, a single CPU performs these functions.Alternatively, separate CPUs may be used or the CPU may be segregated toperform the described functions.

[0033] The invention is described herein in connection with MESS indicesimplemented by Credit Suisse First Boston (“CSFB”), a global investmentbank providing securities underwriting, sales and trading, investmentbanking, private equity, financial advisory and other related services.There are sixty four (64) different MBS indices currently developed byCSFB. This application discloses the invention with regard to thegeneric MBS Index (ire., TBA Mortgage Index), unless otherwisespecified. As will be apparent to one of ordinary skill in the art, thealgorithm may be modified to generate and manage different MBS indices.This disclosure provides examples of such possible modifications whereappropriate. For example, individual weight-calculating formulas areprovided for Conventional, Government, 30-year and 15-year indices.

[0034]FIG. 4 is a flow chart of the method of the present invention. Themethod may be implemented by a general purpose computer operating inaccordance with an algorithm 10 for generating, evaluating andrebalancing a generic MBS Index (i.e., TBA Mortgage Index). Inaccordance with the preferred embodiment of the present invention, alloutstanding mortgage-backed securities are considered in block 12, inorder to generate a generic MBS Index. These p securities are eitherincluded or excluded from the Index based on their total principaloutstanding. Equations 1.1 and 1.2 describe the conditions for inclusionand elimination of MBS securities. The relative weights are thenassigned to each included security, in block 14, in accordance withEquation 1.3. To evaluate the performance of the provided Index over adesired time interval, a total return for each pass-through present inthe Index during this time interval is first determined, block 16. Thistotal return of each generic pass-through is calculated in accordancewith Equation 4.1. Using these total returns for all generic securitiescalculated in block 16, the total return of the Index can be determinednext, at block 18, using one of the Equations 2.1, 2.2 or 2.3, dependingon the length of the desired time interval.

[0035] In accordance with the preferred embodiment, each provided Indexmay also be characterized by its level. The level of the Index is basedon the total return of the Index over the life of the Index (or anyother desired time interval) and is calculated in block 20 usingEquations 6.2 and 6.3. Each Index is then rebalanced in block 22,preferably on the last business day of each month, by repeating theabove steps 12 through 20 (blocks 12-20 of FIG. 4).

[0036] Referring specifically to the operations to be performed inblocks 12 and 14, Equations 1.1, 1.2 and 1.3 present the algorithm forincluding and excluding bonds in the TBA Mortgage Index as well as themethod of assigning relative weights to the generic pass-throughsincluded in the Index. As described further below, this algorithm may bemodified in the process of creating non-generic indices, for example,the Conventional, Government, 30-year, and 15-year indices. As will beobvious to one of ordinary skill in the art, other MBS indices may alsobe created based on the provided generic algorithm.

[0037] Generic mortgage-backed securities are preferably differentiatedby agency, coupon, and original term only. Before the relative weightsare computed, the composition of the Index has to be ascertained, i.e.,it has to be determined which securities to include in the Index andwhich to exclude from the Index. For this purpose, all TBA-eligiblepools (i.e., pools of mortgage-backed securities eligible for“to-be-announced” transactions) should be considered. TBA-eligible poolsare defined by the Bond Market Association (also referred to in thepresent disclosure as PSA, i.e., Public Securities Association), andthese definitions are incorporated herein by reference. TheseTBA-eligible pools will preferably include mortgage-backed securitiesissued by FNMA, GNMA I (i.e., modified pass-through mortgage-backedsecurities on which registered holders receive separate principal andinterest payments on each of their certificates), GNMA II (i.e.,modified pass-through mortgage-backed securities on which registeredholders receive an aggregate principal and interest payment from acentral paying agent on all of their Ginnie Mae II MBS), and/or FHLMC,all with fixed-rate coupons and original terms of 30 or 15 years. Thesepools are preferably aggregated based solely on coupon and originalterm. The original year term and the coupon value may be preprogrammedin the system or may be input into the system as operating parameters.Additional information related to these MBS may also be preprogrammed orinput into the system.

[0038] In accordance with the preferred embodiment, if the totalprincipal outstanding of any 30-year coupon represents more than 1.5% ofthe total outstanding principal for all considered pools, then that30-year coupon will be included in the Index. Likewise, if the totalprincipal outstanding on any 15-year coupon represents more than 0.4% ofthe total outstanding principal for all considered pools, then that15-year coupon will be included in the Index. For example, if 30-yearcoupons having value of 8.5% represent more than 1.5% of the totalprincipal outstanding, then FNMA 8.5, GNMA 8.5 and FHLMC 8.5 are allincluded in the generic TBA Mortgage Index. If, collectively, theyrepresent less than 1.5% of the total outstanding, then none of thesegeneric securities is included in the Index. The percentages (i.e., the1.5% and 0.4% thresholds values) for each coupon term may bepreprogrammed in the system or input into the system as operatingparameters. In an alternative embodiment, after the above conditions aresatisfied, the Index may include only the top six 30-year coupons andthe top six 15-year coupons, as ranked by their outstanding principals.The number of coupons to be included in the index may also bepreprogrammed or input into the system.

[0039] The data regarding outstanding principal amounts may becontinuously streamed into the system or input into the system when itbecomes available. The above calculations are preferably performedduring the second full business week of each month, when the agencies'data becomes available, in order to determine which bonds to include inthe Index as of the close of the last business day of that month. Itshould be noted that inclusion in one month does not guarantee inclusionin the next month. The time for performing the above calculations (i.e.,the second full business week) may be preprogrammed in the system orinput into the system as an operating parameter.

[0040] The total principal outstanding in a TBA eligible pool issued byagency a with a coupon c and original term t as of the first of eachmonth is referred to herein as ρ_(a,c,t), and, as noted above, ispreferably calculated in the second week of that month for eachfixed-rate agency pass through. Therefore, for each coupon and originalterm, the inclusion criterion x_(c,t) may be defined by the followingequations:

x_(c,360)=1 if x_(c,360)>1.5%

x_(c,180)=1 if x_(c,180)>0.4%

x_(c,t)=0 otherwise,  (Eq. 1.1)

[0041] with $\begin{matrix}{x_{c,t} = \frac{\lbrack {\sum\limits_{a = {\{\begin{matrix}{FNMA} \\{GNMA} \\{FHLMC}\end{matrix}\}}}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}} & ( {{Eq}.\quad 1.2} )\end{matrix}$

[0042] The system determines the composition of the index based on thepreprogrammed values, operating parameters and the agencies' inputprincipal data in accordance with the above equation to perform step 12of FIG. 4.

[0043] After deciding which generic mortgage-backed securities are to beincluded in the Index, the relative weight of each generic pass-throughmay be assigned (step 14 of FIG. 4). In accordance with the presentinvention, the relative weights are based on the relation of the currentoutstanding principal of the considered generic pass-through to thetotal outstanding principal represented in the Index and are preferablyexpressed in percentage terms. These weights represent the relativeproportions of different generic fixed-rate agency pass-throughs in thegeneric Index. In accordance with this embodiment, Equation 1.3mathematically defines the weight of each generic pass-through in thegeneric TBA Mortgage Index as a function of agency, coupon, and originalterm as: $\begin{matrix}{w = \frac{\lfloor {x_{c,t}\rho_{a,c,t}} \rfloor}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}} & ( {{Eq}.\quad 1.3} )\end{matrix}$

[0044] Although the relative weights are preferably calculated duringthe second week of each month, they preferably become effective as ofthe close of the last business day of the month in which the calculationtook place. The time for calculating the relative weights and the timethey become effective may be preprogrammed in the system or input intothe system as operating parameters. To ensure reliability of the dataused in the disclosed calculations, the sources of all data pertainingto outstanding principals should be the agencies themselves. On the lastbusiness day of each month, a set of weights for each index is output orotherwise published.

[0045] The above algorithm for including and excluding genericpass-throughs and for calculating their relative weights within thegeneric MBS Index may be modified to produce the weights of theConventional, Government, 30-year, and 15-year indices. An operationparameter may be input into the system to signal this modification inthe provided method. For the Conventional Pass Through Index, whencomputing the weights using Equation 1.3, all weights assigned to GinnieMae pass-throughs are set to 0 during the final, step. Similarly, whencomputing the weights for the Ginnie Mae (i.e., “Government”)Pass-Through Index using Equation 1.3, all weights assigned tonon-Ginnie Mae pass-throughs are set to 0 during the final step. Whencomputing the weights for the 30-Year Pass-Through Index using the abovealgorithm, all weights assigned to 180-month original term pass-throughsare set to 0 during the final step. Similarly, when computing theweights for the 15-Year Pass-Through Index using the above algorithm,all weights assigned to 360-month original term pass-throughs are set to0 during the final step. Therefore, when total returns of these indicesare calculated, total returns from the excluded securities will be equalto “0,” and only returns from the included securities will be consideredand outputted from the system. Thus, even though all outstandingmortgage-backed securities will be considered in the initial selectionprocess, the total return, level and other performance characteristicsprovided to an end user will only relate to the desired Index. Forexample, if the user desires to receive information about performance ofthe 30-year MBS Index, total returns from all 15-year securities will beequal to “0” and the displayed characteristics will only relate to30-year mortgage-backed securities.

[0046] With respect to step 18 of FIG. 4, one of the maincharacteristics of each of the provided indices is its total return. Forlimited periods of time, the total return of each index may be definedas an average total return of the bonds represented in that index.Hence, to calculate the total return over a short period of time it isfirst necessary to calculate which bonds are represented in the indexduring that time period, using the algorithm described above, andsecond, to calculate the return of each bond. For longer periods of timethe total return is computed by compounding over a set of disjoint andcomplete subintervals of time.

[0047] As described above, on the last business day of each month a setof relative weights for issues included in the Index is introduced. Forthe month following the month when calculations took place these weightsrepresent relative proportions of each pass-through selected to be inthe Index. Therefore, from the last business day of any month to anybusiness day of the following month, a fixed portfolio can represent theIndex. Accordingly, over this time period the Index total return isequal to the total return of the representative portfolio. For longertime intervals, representative portfolios may be used to calculate themonth-to-month returns. Compounding these returns gives the Index returnover several months.

[0048] For example, to calculate the Index total return from Oct. 14,2000 until Dec. 15, 2000, representative portfolios may be used tocalculate the total returns for the months of Oct. 14, 2000 to Oct. 31,2000, of Oct. 31, 2000 to Nov. 30, 2000, and of Nov. 30, 2000 until Dec.15, 2000. The product of these three numbers is the Index total returnfrom Oct. 14, 2000 to Dec. 15, 2000. The total return from Oct. 14, 2000until Oct. 31, 2000 is the total return of the representative portfoliofrom Sep. 29, 2000 to Oct. 31, 2000 minims the return from Sep. 29, 2000to Oct. 13, 2000.

[0049] To express the above example in algebraic form, consider a datet₁ in month k and a later date t₂ in month n. When k=n, the total returnof the Index from the close of t₁ until the close of t₂ is,

TR| _(t) ₁ ^(t) ^(₂) =TR _(t) ₂ −TR _(t) ₁   (Eq. 2.1),

[0050] where TR_(t) ₁ is the month-to-date total return of said index onthe day t₁, and TR_(t) ₂ is the moth-to-date total return of said indexon the day t₂.

[0051] Or when k=n−1,

TR| _(t) ₂ ^(t) ^(₂) =(1+TR _(k) −TR _(t) ₁ )(1+TR _(t) ₂ )−1  (Eq.2.2),

[0052] where TR_(k) is the total return of the Index for the month k.

[0053] Or when k<n−1, $\begin{matrix}{{{{T\quad R}|_{t_{1}}^{t_{2}}} = {{{( {1 + {T\quad R_{k}} - {T\quad R_{t_{1}}}} )\lbrack {\prod\limits_{i = {k + 1}}^{n - 1}( {1 + {T\quad R_{i}}} )} \rbrack}( {1 + {T\quad R_{t_{2}}}} )} - 1}},} & ( {{Eq}.\quad 2.3} )\end{matrix}$

[0054] where TR_(i) is the total return of the Index for anyintermediate month between k and n. In the preferred embodiment, TR_(i)is the total return of the Index from the close of the last business dayof the month i−1 to the close of the last business day of the month i.Both TR_(i) and TR_(t) are defined in Equations (3.1) and (3.2).Equations 2.1, 2.2 and 2.3 define the operations to be performed in step18 of the flow chart of FIG. 4.

[0055] From the end of one month to the end of the next month, the totalreturn of the Index is defined by the total return of a fixedrepresentative portfolio. To compute the return of a representativeportfolio one has to calculate the cost of buying the portfolio,same-day settle on the earlier date; the gain from selling theportfolio, same-day settle on the later date; and the value of any paydowns earned.

[0056] Let the set {w_(i)^(j)}_(j = 1)^(n)

[0057] be the relative weights of the securities composing the genericIndex as of the close of the last business day of month i−1. Then thetotal return of the Index from the close of the last business day of themonth i−1 until the close of the last business day of month i is,$\begin{matrix}{{{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i\quad i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},} & ( {{Eq}.\quad 3.1} )\end{matrix}$

[0058] where TR_(t) ^(j) is the total return of generic pass-through jover this time interval as will be shown in Equation 4.1, discussed withrespect to step 16 of FIG. 4. The Equation 3.1 may be rewritten forTR_(k) as: $\begin{matrix}{{{T\quad R_{k}} = \frac{\sum\limits_{j = 1}^{n}{w_{k}^{j}p_{k}^{j}T\quad R_{k}^{j}}}{\sum\limits_{j = 1}^{n}{w_{k}^{j}p_{k}^{j}}}},} & ( {{Eq}.\quad 3.3} )\end{matrix}$

[0059] The price of each pass-through is preferably the same-day settleprice, measured on close of the last business day of month i−1 (or k−1),and is denoted p_(i) ^(j) (or p_(k) ^(j) or simply p_(i)). Itscomputation is described further below (see Equations 5.1-5.5).

[0060] For any arbitrary business day t in any month i: $\begin{matrix}{{{T\quad R_{t}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},} & ( {{Eq}.\quad 3.2} )\end{matrix}$

[0061] where TR_(t) ^(j) is the total return of generic pass-through jfrom the close of the last business day of the month i−1 until the closeof the business day, t.

[0062] As shown in FIG. 4, step 16, in order to calculate the totalreturn of the Index, the total return of each generic pass-through hasto be calculated first. In accordance with the preferred embodiment ofthe present invention, formulas for calculating the total return of eachpass-through in the index for specific time periods are provided. Thetotal return calculations involve buying and selling securities for thesame-day settle price, however, the only prices observable in themarketplace are for the standard PSA (i.e., TBA) settle prices.Consequently the standard formulas typically used in the industry arebased on PSA settle prices. In contrast, the method of calculating thetotal return of each pass-through in accordance with the presentinvention uses formulas which are based on the same-day settle prices,not standard PSA settle prices. Therefore, a conversion algorithm isprovided by the present invention, as more particularly described inconnection with Equations 5.1-5.5.

[0063] Consider a mortgage-backed security of coupon c. At the close ofthe last business day of a month an investor purchases $1 of thesecurity for price p₁. On the close of an arbitrary business day of thefollowing month the investor sells the remaining principal for price p2.The investor receives the coupon payment, $\frac{c}{12}$

[0064] and the pay down (1−f) due the month of sale, which is investedat rate r. These numbers suffice to calculate the total return of thissecurity.

[0065] For a generic pass-through j, of fixed-rate coupon c, the totalreturn from the close of business on the last business day t₁ of onemonth, to the close of business on an arbitrary business day, t₂, in thenext month is defined as: $\begin{matrix}{{T\quad R_{t_{2}}^{j}} = \frac{{- p_{t_{1}}} + {f_{t_{1}}p_{t_{2}}} + {\lbrack {( {1 - f_{t_{1}}} ) + \frac{c}{12}} \rbrack \lbrack {1 + {r_{t_{1}}\frac{|d|}{360}}} \rbrack}^{- k}}{p_{t_{1}}}} & ( {{Eq}.\quad 4.1} )\end{matrix}$

[0066] The terms on the right hand side are:

[0067] p_(t)=price of the security on the close of t, same-day settle.

[0068] r_(t)=1-month BBA LIBOR on the close of t (provided by Reuters).

[0069] f_(t)=the pay-down factor of the pass-through as best determinedby day t. $\begin{matrix}{d\{ {= \begin{matrix}{\quad {{25 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {bond}\quad {FNMA}}}\quad} \\\quad \\\quad \\{\quad {{15 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {bond}\quad {GNMA}\quad {or}{\quad \quad}{FHLMC}}}}\end{matrix}} } \\{k\{ {= \begin{matrix}{{+ 1},} & {{{if}\quad d} > 0} \\\quad & \quad \\\quad & \quad \\{{- 1},} & {{{if}\quad d} < 0}\end{matrix}} }\end{matrix}$

[0070] Data for all of these terms is preferably input into the system.

[0071] The algorithm for computing f_(t) is provided in Equation 4.3.Prices, rates, and coupons are preferably all considered as decimals,not percents. If t₂ is the last business day of month i, it can bewritten:

TR_(i) ^(j)=TR_(t) ₂ ^(j)  (Eq. 4.2)

[0072] For a specific mortgage pool, the pay down for month i ispreferably determined by the actual loans represented in the pool duringmonth i−1. Therefore, two separate pools with the same characteristicscan have different total returns.

[0073] In the preferred embodiment of the present invention, the Indexrepresents generic pass-throughs, that is, pass-throughs representativeof all pools of the same coupon, and original term, issued by the sameagency. The total return of a generic pass-through is a weighted averageof all of the pass-throughs it represents.

[0074] For month i, the factor of the generic pass-through with couponc, original term t, issued by agency a may be determined by thefollowing algorithm. First the working set is defined as all MBS poolsissued by the agency a, of original term t, with fixed coupon c as ofthe first of month i. With this set, the maximum WALA (Weighted AverageLoan Age) for TBA pools will be defined as:${n_{cutoff} = {\min \{ {n:{\frac{{{principle}\quad {of}\quad {pools}\quad {with}\quad {WALA}} \leq n}{{principle}\quad {of}\quad {all}\quad {pools}} \geq {2.5\%}}} \}}},$

[0075] with all numbers as of the first of month i+1, then the subset ofTBA pools will be

A={pools: WALA≦n _(cutoff) as of the first of the month i+1}.

[0076] Using this set the pay-down factor of month i is calculated as:$\begin{matrix}{f_{i} = \frac{{\sum\limits_{\alpha \in A}\rho_{\alpha,i}} - {\sum\limits_{\alpha \in A}\rho_{\alpha,{i + 1}}}}{\sum\limits_{\alpha \in A}\rho_{\alpha,i}}} & ( {{Eq}.\quad 4.3} )\end{matrix}$

[0077] with ρ_(α,i) as the principal outstanding of pool α as of thefirst of month i. If the WALA of a pool is unknown, it is estimatedusing CAGE.f_(i) is the generic pay-down factor for the month i.Equation 4.3 creates a sequence of monthly pay-down factors for eachgeneric pass-through. For a specific date t in month i, the pay-downfactor of a generic pass-through as best known by t is preferablydenoted f_(t). The value f_(t) is preferably the latest factor thatwould be known as of the close of t. For example if f_(i) is known by t,then f_(t) is defined as f_(i). Or else, if f_(i−1) is known by t, thenthe f_(t) is defined to be f_(i−1). Alternatively, the f_(t) will bedefined as f_(i−2). The advantage of the above definition of f_(t) isthat it makes the Index independent of subjective prepayment models.Data related to each term found in Equation 4.3 is preferably input intothe system so that the above calculations may be performed.

[0078] As described above, the provided formulas for calculating thetotal return of the Index is based on the same-day settle price, notstandard PSA settle price. As shown for example in FIG. 3, the BondMarket Association announces the MBS settlement dates on which allpurchasing transactions have to be settled. However, if the formula forcalculating the total return of each generic pass-through is based onthis TBA (or PSA) price, the calculation will necessarily include someelement of estimating future cash flows. Consequently, in accordancewith the preferred embodiment of the present invention, the formulas forconverting from standard PSA settle prices to same-day settle prices areprovided. As explained above, standard PSA settle price is the marketobserved price. Equations 5.1-5.5 provide: formulas for converting thestandard PSA settle price, 1-month forward, to the same-day settleprice. Data related to each term found in Equations 5.1-5.5 ispreferably input into the system so that the above calculations may beperformed.

[0079] There are two major differences between quoting prices withstandard PSA settle and with same-day settle. First, standard PSA settleassumes that, while the price is agreed upon today, no payment is madeuntil sometime in the future. Same-day settle requires payment today.Therefore a PSA settle price includes some time value that must bediscounted to convert to today's dollars. Second, pass-throughs beginpaying principal and interest to the bondholder the month followingsettlement. Therefore, purchasing securities 1-month forward standardPSA settle entitles the buyer to the pay down two months after thepurchase day and not the pay down one month after the purchase date. Forsame-day settle the buyer is entitled to both of these pay downs.

[0080] Let {tilde over (p)} represent the standard PSA settle price fora given TBA pass-through on a given date. The dirty price of thatsecurity (actual number of dollars expected for $1 of principal) is,$\begin{matrix}{\overset{\sim}{p} + {\frac{c}{12}\frac{d_{1}}{360}}} & ( {{Eq}.\quad 5.1} )\end{matrix}$

[0081] where c represents the coupon of the pass-through expressed as adecimal (e.g. 7% implies c=0.07), d₁ represents the number of days intothe month that 1-month forward standard PSA settle occurs. For example,if the standard PSA settlement for June 2000 is the 13th, then for anydate in May 2000, d₁=12.

[0082] Discounting this price to the day in question, the followingformula is derived: $\begin{matrix}{\frac{\overset{\sim}{p} + {\frac{c}{12}\frac{d_{1}}{360}}}{1 + {r\frac{d_{2}}{360}}},} & ( {{Eq}.\quad 5.2} )\end{matrix}$

[0083] where r represents the discount funding rate; and d₂ representsthe number of days in between the purchase date and the standard PSAsettle date 1-month forward inclusive of the former and exclusive of thelatter. The rate is quoted as a decimal, e.g. a rate of 6.5 percent iswritten as 0.065.

[0084] The value of the pay down and interest for the month followingthe purchases date is the sum of the two payments (discounted),$\begin{matrix}{\frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}},} & ( {{Eq}.\quad 5.3} )\end{matrix}$

[0085] with f representing the factor (derived from Equation 4.3) forthat bond for that month. In the above equation, d₃ represents thenumber of days between the purchase date and the 25th of the next month(for FNMA MBS) or the 15th of the next month (for GNMA or FHLMC MBS),inclusive of the former and exclusive of the latter.

[0086] Assuming business day t falls in month i, the same-day settleprice for a pass-through at the close of business on t, denoted byp_(t), can be calculated by combining (5.2) and (5.3) ((5.2) is modifiedbecause (5.3) represents some of the principal). The following equationis then derived: $\begin{matrix}{{p_{t} = {{\frac{{\overset{\sim}{p}}_{t} + {\frac{c}{12}\frac{d_{1}}{30}}}{1 + {r\quad \frac{d_{2}}{360}}}f_{t}} + \frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}}}},} & ( {{Eq}.\quad 5.4} )\end{matrix}$

[0087] with {tilde over (p)}_(t) being the TBA price of a pass-through1-month forward standard PSA settle on the close of business on t, asquoted for example by the CSFB Pass-Through desk. The pay-down factor ofthe pass-through as best determined by t, f_(t), is selected from thesequence of monthly pay-down factors derived from the Equation 4.3. Inthis preferred embodiment, r is a 1-month BBA LIBOR (British BankersAssociation London Interbank Offered Rate) at the close of date t, if tis the last business day of the month. If not, then r is 1-month BBALIBOR at the close of the last business day of month i−1. d₁ is thenumber of days between the first of month i+1 and the standard PSAsettlement date in month i+1 inclusive of the later and exclusive of theformer. The number of days between t and the standard PSA settlementdate of month i+1 inclusive of the former and exclusive of the latter isshown in the (5.4) as d₂. For FNMA pass-throughs, d₃ is the number ofdays between the 25th of month i+1 and t inclusive of the former andexclusive of the latter. For GNMA and FHLMC pass-throughs, d₃ is thenumber of days between the 15th of the month i+1 and date t, inclusiveof the former and exclusive of the latter. The values {tilde over(p)}_(t), r_(t), and c are often quoted as percents, however, in (5.4)they are all decimals. The source of 1-month BBA LIBOR is Reuters, andis defined in BRITISH BANKERS' ASSOCIATION (2000) Libor OfficialDefinition (incorporated herein by reference). The BBA LIBOR and itsdefinition may also be found at www.BBA.ORG.UK. The source of the PSAsettlement dates is The Bond Market Association and may be obtained fromwww.bondmarket.com, as shown for example in FIG. 3.

[0088] When t is the last business day of the month i−1:

p_(t)=p_(i),  Eq. 5.5

[0089] In accordance with the preferred embodiment of the presentinvention, each index may be characterized by its level. The level ofthe Index is defined by Equations 6.2 and 6.3 and is calculated in step20 in FIG. 4. It should be noted that level determination is not arequired step of the present invention, and any other tool known in theart may be used with the provided MBS Index to evaluate its performance.

[0090] In accordance with the preferred embodiment, the starting date ofthe index is input into the system. Equation 6.2 sets a starting levelfor this chosen starting date. Equation 6.3 sets the percent levelchange between two days to be the total return of the Index betweenthose two days. The total return of the Index is determined from theEquations 2.1, 2.2 or 2.3 above.

[0091] The level is a useful tool for evaluating an investment in theIndex. Assuming monthly reinvestment in the Index, a cash investment of$X on the date t₁ will show either a profit or a loss by a latter datet₂ such that $\begin{matrix}{{\$ \quad x\frac{P_{t_{2}} - P_{t_{1}}}{P_{t_{1}}}},} & ( {{Eq}.\quad 6.1} )\end{matrix}$

[0092] where P_(t) is the level of the Index on day t. Of course, theinvestor's true total return will depend on how the monthly payments arereinvested.

[0093] If on the close of 12/31/93 the initial level of the Index isdefined as:

P_(12/31/93)=100  (Eq. 6.2),

[0094] then on the close of any subsequent date t the level will be$\begin{matrix}{{\frac{P_{t}}{P_{{12/31}/93}} = {{1 + {TR}}|_{{12/31}/93}^{t}}},} & ( {{Eq}.\quad 6.3} )\end{matrix}$

[0095] where TR|_(12/13/93) ^(t) is the total return of the Index fromthe close of 12/31/93 until the close of t. Over time movements in thelevels are determined by the total return of the indices. Of course, thedate 12/31/93 is selected arbitrarily and may be substituted by theactual start date of the index.

[0096] In accordance with the preferred embodiment of the presentinvention, a system 50 for generating and managing an MBS Index isprovided to perform the above described method. FIG. 2 is a functionalblock diagram of an embodiment of the invention showing discretecomponents and information flow within the system 50. To accomplishe thedescribed steps of the algorithm 10, system 50 preferably comprises amarket data input device 26 (which may include an input/output interface2 and input device 3, as shown in FIG. 1) for imputing necessary datarelated to outstanding mortgage-backed securities. Such data willinclude original term, coupon value, issuing agency, and outstandingprincipal on each outstanding mortgage-backed security. Additional datainputs into the system 50 through the market data input 26 preferablyinclude TBA settle prices, PSA settle dates and BBA LIBOR rates.

[0097] The input data received by the system from the input 26 ispreferably classified in the classification processor 28. Theclassification processor 28, which may be part of the CPU 1 shown inFIG. 1, classifies all outstanding mortgage-backed securities inaccordance with their original term, coupon value, and issuing agency.Classified securities are then aggregated into pools in accordance withtheir coupon and original term. The data and composition of allaggregated pools are then outputted from the classification processorinto the central hub 24. As will be obvious to one of ordinary skill inthe art, it is not necessary to include the central hub 24 into thesystem 50, and all described data transfers may be accomplished bydirectly connecting the discrete components of the system to each other.Input processors 28-42 of FIG. 2 may all be included in the single CPU 1of FIG. 1.

[0098] The central hub 24 is preferably connected to an Index database44 for storing data related to the provided MBS Index. The Indexdatabase 44 may also store some tentative data, for example results ofintra-step calculations, for future use. Although shown as a singlecomponent in FIG. 2, the Index database may comprise several components,for example, RAM 5, shown in FIG. 1, a hard drive, a connected zip driveor a separate database server. Output of every discrete component of thesystem 50 is preferably input into the central hub 24 and is furthertransmitted into the Index database 44. Selected data stored in theIndex database may be outputted to the output terminal 46. The outputterminal may include or be connected to the input/output interface 6 andthe output device 7 as shown in FIG. 1.

[0099] On the last business day of month i, the composition of allaggregated pools and other data related to these pools is input into anIndex composition processor 30 from the central hub 24. The logic flowchart of the processing logic for the index composition determination isshown in FIG. 5. Logic conceptually begins at block 301 and proceeds toblock 302 where the aggregated pools and their associated data areentered into the composition processor. At block 303, based on the inputdata, a total outstanding principal for all aggregated pools iscalculated. One of the aggregated pools is selected for determination inblock 304, and its outstanding principal is calculated in block 305. Theresults of calculations of blocks 303 and 305 are input into block 306,where the inclusion criterion is determined in accordance with Equation1.2. At logic block 307, the processor will determine the original termof the pool selected in 304 and, if the original term is 30-years (360months), the inclusion criterion x_(c,t) is compared to 1.5% at logicblock 308. If however, the original term is 15 years (180 months) theinclusion criterion is compared to 0.4% at logic block 309. Aggregatedpools having a 30-year original term are included in the Index at block311 if the expression at block 308 is determined to be true. Aggregatedpools having a 15-year original term are included in the Index at block311 if the expression at block 309 is determined to be true. Otherwise,the pool is discarded at block 310. After either the inclusion orexclusion of the pool selected in 304, the process is repeated fromblock 304 until all aggregated pools are considered. The Indexcomposition, i.e., a list of all selected securities, is outputted intothe central hub 24 and stored in the Index database 44, preferably witha month for which this Index was generated. As explained above, thecomposition of the Index will remain constant for one month. On the lastbusiness day of the next month the index composition processor isactivated again and the selection process repeats.

[0100] Relative weights of each mortgage-backed security included in theIndex are preferably calculated in the weights processor 32, FIG. 2. Thelogic flow chart of the processing logic for the weights determinationis shown in FIG. 6. Logic conceptually begins at block 321 and proceedsto input block 322 where the inclusion criteria from block 306 and totaloutstanding principal on each selected security from market data input26 of FIG. 2 are entered into the weights processor. Total outstandingprincipal on all securities included in the Index is calculated at block323, and the relative weight of each security is determined at block 324using the Equation 1.3. The relative weights are outputted from theweights processor 32, input into the central hub 24 and preferablystored in the Index database 44.

[0101] In the preferred embodiment, the system 50 is also provided witha date calculator and internal calendar 38. As described above inconnection with steps 16 and 18 of the algorithm 10, shown in FIG. 4,various dates and differences between them are used to calculate factorf_(t), total return of each pass-through, total return of the Index,same-day-settle price and level of the Index. As would be obvious to oneof ordinary skill in the art, these dates may be observed in the marketand if the differences between them are required for furthercalculations, these differences can be determined within the individualprocessors, where these further calculations are to be performed.However, for purposes of efficiency it is preferred that the date onwhich each calculation is performed (also referred to in this disclosureas “the current date” and “t₂”) is determined by the provided internalcalendar. It is also preferred that all manipulations and calculationsinvolving dates are made in the provided date calculator associated withthe internal calendar. For example, instead of calculating the term dtwice, as this term is required in the calculations of total return ofeach individual pass-through and same-day-settle price (in block 34 andblock 42 of FIG. 2), it can be calculated once in the date calculator 38and then input into blocks 34 and 42 when necessary.

[0102] Pay-down factor f_(i) for each month is calculated in the factorprocessor 40 of FIG. 2. The logic flow chart of the processing logic forthe factor determination is shown in FIG. 7. Logic conceptually beginsat block 401 and proceeds to input block 402 where the total outstandingprincipal on each selected security is entered into the factorprocessor. The outstanding principal data may be input at 26 of FIG. 2or may already be stored in the Index database 44 during performance ofprior operations (e.g. steps 12 and 14 of FIG. 4). Principal outstandingof all securities within pool α for month i is calculated at block 403,and principal outstanding of all securities within pool α for month i+1is calculated at block 404. These outstanding principals for twoconsecutive months are then input into the factor calculator 405, wherethe pay-down factor is determined in accordance with Equation 4.3. Thepay-(town factor f_(i) is outputted from the factor processor 40, inputinto the central hub 24 and stored in the Index database 44.

[0103] Same-day-settle price for each security is calculated in thesame-day-settle price processor 34 of FIG. 2. The logic flow chart ofthe processing logic for the determination of these prices is shown inFIG. 8. Logic conceptually begins at block 341 and proceeds to inputblock 342 where the 1-month BBA LIBOR, TBA price, and coupon value ofeach security included in the Index is entered into the same-day-settleprice processor from the market data input 26 of FIG. 2. Additionally,date differences d₁, d₂ and d₃ are entered into the input block 342 fromthe date calculator 38. In block 343 the latest known pay-down factorf_(t) is selected from the Index database 44 where all pay-down factorsare stored. Using the input data, the same-day-settle price calculator34 determines this price in accordance with Equation 5.4 in block 344.The same-day-settle price is outputted from its processor 34, input intothe central hub 24 and stored in the Index database 44. The abovedescribed algorithm is repeated for every security included into theIndex in the month of calculations.

[0104] Total return of the Index from the date t₁ of month k to date t₂of month n is calculated in the total return processor 42 of FIG. 2. Thelogic flow chart of the processing logic for the total returndetermination is shown in FIG. 9. Logic conceptually begins at block 421and proceeds to input block 422 where all necessary dates anddifferences between them are entered from block 38, coupon values andBBA LIBOR rates are entered from input 26 (or from the Index database 44if these rates were previously stored there), same-day-settle prices areeither entered from block 34 or retrieved from the database 44, thelatest known pay-down factor is retrieved from the database 44, and therelative weights are either entered from block 32 or retrieved from thedatabase 44. Total return of each individual pass-through in the Indexis calculated at block 423 in accordance with Equation 4.1. Totalreturns of the Index for individual months (TR_(i)) are eithercalculated at block 424 in accordance with Equation 3.1 or retrievedfrom the database 44 if available, and total returns of the Index fromthe first of the month until a desired date (e.g. t₁ or t₂) within thatmonth are calculated at block 425 in accordance with Equation 3.2. Thesecalculated total returns are then input into the logic block 426. Totalreturns for individual months are preferably also outputted for storagein the database 44 so that they can be later retrieved from the databasewithout repeating the above calculations. At logic block 426, theprocessor will determine the difference between the months k and n. If kand n are the same month (i.e., k=n), the total return of the indexbetween t₁ and t₂ is calculated at block 427 according to Equation 2.1.If k and n are not the same, the system will proceed to logic block 428where the system will determine whether k and n are consecutive months(i.e., k=n−1). If k and n are in fact consecutive, the processor willcalculate the total return of the Index at block 429 using Equation 2.2.Alternatively, the processor will calculate the total return of theIndex at block 430 using Equation 2.3. The output of blocks 427, 429 and430 is preferably input into the database 44 for storage. Additionally,in accordance with the preferred embodiment, a month-to-day total returnof the Index is outputted onto the output terminal 46 as a benchmarkmeasuring the performance of the provided MBS Index.

[0105] System 50 is further provided with a level processor 36 where thelevel of the Index is determined in accordance with Equation 6.3. Thestarting level of the Index is preferably arbitrarily assigned, storedin the database 44 and retrieved for calculations by the level processor36 when necessary. The total return for the life of the index may becalculated in the A total return processor 42 and input into the levelprocessor 36. The resulting level of the Index is input into the centralhub 24 and stored in the Index database 44. Additionally, in accordancewith the preferred embodiment, a daily level of the Index is outputtedonto the output terminal 46 as a benchmark measuring the performance ofthe provided MBS Index. Any other variable stored in the Index database44 may also be displayed on the output terminal 46 if desired.

[0106] MBS Indices provided in accordance with the present invention maybe used as a benchmark for objectively and accurately measuring theperformance of the MBS sector of the market. The indices will preferablybe published, or otherwise made available, on a monthly basis. Themethod provided by the present invention for generating MBS indices maybe used by portfolio managers for creating index funds mirroring orreflecting the provided MBS indices. The algorithm may be encoded into acomputer program and distributed to users on a CD-ROM or anotherreadable storage device. Alternatively, this MBS index-generatingprogram may be stored on a web server or an enterprise server andstreamed, downloaded or otherwise provided to interested users on anas-needed basis. Since the composition of each index is preferably heldconstant throughout a month, fund managers avoid the need to match theprovided benchmark's moves on a daily basis. Additionally, the providedsystem and method allow users to easily and automatically rebalance theindex at or near the end of the month.

[0107] Having described this invention with regard to specificembodiments, it is to be understood that the description is not meant asa limitation since further variations or modifications may be apparentor may suggest themselves to those skilled in the art. For example, theprovided method may easily be modified to generate other types of MBSindices. It is intended that the present application cover suchvariations and modifications as fall within the scope of the appendedclaims.

What is claimed is:
 1. A method for managing a mortgage-backedsecurities index, comprising the steps of: a. selecting a set ofmortgage-backed securities to be included in said mortgage-backedsecurities index, said set of mortgaged-backed securities being selectedfrom all outstanding mortgage-backed securities; b. assigning a relativeweight to each security within said selected set, said relative weightbeing a relative proportion of total outstanding principal on said eachsecurity to the total outstanding principal on all securities withinsaid selected set; c. calculating a total return of said mortgage-backedsecurities index, said total return being based on said assignedrelative weight for said each security, and a total return of said eachsecurity based on a same-day-settle price.
 2. A method for managing amortgage-backed securities index according to claim 1, wherein said stepof selecting a set of mortgage-backed securities further comprises stepsof. a. aggregating said all outstanding mortgage-backed securities in toa plurality of pools, each of said pools comprising mortgage-backedsecurities having the same coupon and the same original term; and b.calculating an inclusion criteria for each pool within said plurality ofpools.
 3. A method for managing a mortgage-backed securities indexaccording to claim 2 wherein said inclusion criteria is given by thefollowing equation:${x_{c,t} = \frac{\lbrack {\sum\limits_{a = {\{\begin{matrix}{FNMA} \\{GNMA} \\{FHLMC}\end{matrix}\}}}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}},$

wherein ρ_(a,c,t) is the total outstanding principal on said outstandingmortgage-backed securities, a is an agency which issued said outstandingmortgage-backed securities, c is a coupon value of said outstandingmortgage-backed securities, and t is an original term of saidoutstanding mortgage-backed securities.
 4. A method for managing amortgage-backed securities index according to claim 3, furthercomprising steps of comparing said inclusion criteria for a particularpool to a threshold value, and including said particular pool in saidselected set if said threshold is met.
 5. A method for managing amortgage-backed securities index according to claim 4, wherein saidthreshold value is 1.5% for all 30-year mortgage-backed securitiespools.
 6. A method for managing a mortgage-backed securities indexaccording to claim 4, wherein said threshold value is 0.4% for all15-year mortgage-backed securities pools.
 7. A method for managing amortgage-backed securities index according to claim 3 wherein saidrelative weight of said each security within said selected set is givenby the$w = {\frac{\lfloor {x_{c,t}\rho_{a,c,t}} \rfloor}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}.}$


8. A method for managing a mortgage-backed securities index according toclaim 7, wherein said total return of said each security within saidselected set on any given day t₂ is given by the following equation:${{T\quad R_{t_{2}}^{j}} = \frac{{- p_{t_{1}}} + {f_{t_{1}}p_{t_{2}}} + {\lbrack {( {1 - f_{t_{1}}} ) + \frac{c}{12}} \rbrack \lbrack {1 + {r_{t_{1}}\frac{|d|}{360}}} \rbrack}^{- k}}{p_{t_{1}}}},$

wherein p_(t) ₁ is a same-day settle price of said each security on theclose of day t₁, wherein p_(t) ₂ is a same-day settle price of said eachsecurity on the close of day t₂, wherein r_(t) ₁ is a one-month BBALIBOR on the close of day t₁, wherein f_(t) ₁ is a monthly pay-downfactor of said each security as best determined by day t₁, said monthlypay-down factor f_(t) ₁ being selected from a sequence of monthlypay-down factors f_(i), t₁ is the last business day of the precedingmonth, t₂ is any day of the current month, and wherein $\begin{matrix}{d = \{ \begin{matrix}{\quad {{25 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}\quad {security}\quad {is}\quad {issued}\quad {by}\quad {FNMA}}}\quad} \\\quad \\\quad \\{\quad {{15 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}{\quad \quad}{security}\quad {is}{\quad \quad}{issued}{\quad \quad}{by}\quad {GNMA}\quad {or}{\quad \quad}{FHLMC}}}}\end{matrix} } \\{and} \\{k = \{ \begin{matrix}{{+ 1},} & {{{if}\quad d} > 0} \\\quad & \quad \\\quad & \quad \\{{- 1},} & {{{if}\quad d} < 0}\end{matrix} }\end{matrix}$


9. A method for managing a mortgage-backed securities index according toclaim 8, wherein said sequence of monthly pay-down factors is given bythe following equation:${f_{i} = \frac{{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}} - {\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,{i + 1}}}}{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}}},$

wherein ρ_(α,i) is the principal outstanding of pool α as of the firstof month i, and wherein ρ_(α,i+1) is the principal outstanding of pool αas of the first of month i+1.
 10. A method for managing amortgage-backed securities index according to claim 9 wherein saidsame-day settle price is given by the following equation:${p_{t} = {{\frac{{\overset{\sim}{p}}_{t} + {\frac{c}{12}\frac{d_{1}}{30}}}{1 + {r\quad \frac{d_{2}}{360}}}f_{t}} + \frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}}}},$

wherein {tilde over (p)}_(t) is the TBA price of said security 1-monthforward standard PSA settle on the close of business on day t; whereind₁ is the number of days into the month that 1-month forward standardPSA settle occurs; wherein d₂ is the number of days in between thepurchase date and the standard PSA settle date 1-month forward inclusiveof the former and exclusive of the latter; wherein, for FNMAmortgage-backed securities, d₃ is the number of days between thepurchase date and the 25th of the next month; wherein for GNMA or FHLMCmortgage-backed securities, d₃ is the number of days between thepurchase date and the 15th of the next month; and wherein r is aone-month BBA LIBOR on the close of day t.
 11. A method for managing amortgage-backed securities index according to claim 10 wherein saidtotal return of said index from day t₁ in month k to day t₂ in month nis given by the following equation:${{{T\quad R}|_{t_{1}}^{t_{2}}} = {{{( {1 + {T\quad R_{k}} - {T\quad R_{t_{1}}}} )\lbrack {\prod\limits_{i = {k + 1}}^{n - 1}( {1 + {T\quad R_{i}}} )} \rbrack}( {1 + {T\quad R_{t_{2}}}} )} - 1}},$

is the month-to-date total return of said index on the day t₁, andTR_(t) ₂ is the moth-to-date total return of said index on the day t₂,wherein TR_(k) is the total return of the index for the month k, andwherein TR_(i) is the total return of the index for any intermediatemonth between k and n.
 12. A method for managing a mortgage-backedsecurities index according to claim 11 wherein said total return of theindex for any intermediate month is given by the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i\quad i}^{j}T\quad R_{t}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein said total returns of said index on the day t₁ and t₂ are givenby the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein {w_(i) ^(j)}_(j=1) ^(n) are the relative weights of saidmortgage-backed securities within said index, and wherein p_(i) ^(j) isthe same-day settle price for said each security within said index. 13.A method for managing a mortgage-backed securities index according toclaim 12, further comprising a step of determining a level of saidmortgage-backed securities index, said level being given by thefollowing equation:${\frac{P_{t}}{P_{{00/00}/00}} = {{1 + {TR}}|_{{00/00}/00}^{t}}},$

wherein P_(00/00/00) is the starting level of said index, whereinTR|_(00/00/00) ^(t) is the total return of said index from start to theday t, and wherein Pt is the current level of the index.
 14. A methodfor managing a mortgage-backed securities index according to claim 13,wherein said starting level of said index is
 100. 15. A method formanaging a mortgage-backed securities index according to claim 1,further comprising a step of rebalancing said index by repeating saidsteps of selecting a set of mortgage-backed securities to be included insaid mortgage-backed securities index, assigning said relative weight toeach security within said selected set, and calculating said totalreturn of said mortgage-backed securities index.
 16. A system formanaging a mortgage-backed securities index, comprising: input means forinputting market data into said system, said market data comprising datafor all outstanding mortgage-backed securities; selection means forselecting a set of mortgage-backed securities to be included in saidmortgage-backed securities index, said set of mortgaged-backedsecurities being selected from said all outstanding mortgage-backedsecurities; weight means for assigning a relative weight to eachsecurity within said selected set, said relative weight being a relativeproportion of total outstanding principal on said each security to atotal outstanding principal on all securities within said selected set;and total return means for calculating a total return of saidmortgage-backed securities index, said total return being calculatedbased on said assigned relative weight of said each security within saidselected set, and a total return of said each security within saidselected set based on a same-day-settle price.
 17. A system for managinga mortgage-backed securities index according to claim 16 furthercomprising a storage means, said storage means storing data circulatedwithin said system.
 18. A system for managing a mortgage-backedsecurities index according to claim 16 further comprising aclassification means, said classification means classifying said datafor all outstanding mortgage-backed securities in accordance with acoupon value, issuing agency and original term of each of saidoutstanding mortgage-backed securities.
 19. A system for managing amortgage-backed securities index according to claim 18 furthercomprising an aggregation means, said aggregation means aggregating saidoutstanding mortgage-backed securities into a plurality of aggregatedpools.
 20. A system for managing a mortgage-backed securities indexaccording to claim 19 wherein said selection means further comprisesmeans for calculating an inclusion criterion for each of said aggregatedpools.
 21. A system for managing a mortgage-backed securities indexaccording to claim 20 wherein said inclusion criterion is given by thefollowing equation:$x_{c,t} = \frac{\lbrack {\sum\limits_{a = {\{\begin{matrix}{FNMA} \\{GNMA} \\{FHLMC}\end{matrix}\}}}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}$

wherein ρ_(a,c,t) is the total outstanding principal on said outstandingmortgage-backed securities, a is an agency which issued said outstandingmortgage-backed securities, c is a coupon value of said outstandingmortgage-backed securities, and t is an original term of saidoutstanding mortgage-backed securities.
 22. A system for managing amortgage-backed securities index according to claim 21, furthercomprising means for comparing said inclusion criterion for all of saidaggregated pools to a threshold value, and including an aggregated poolin said selected set if said threshold is met.
 23. A system for managinga mortgage-backed securities index according to claim 22, wherein saidthreshold value is 1.5% for all 30-year mortgage-backed securitiespools.
 24. A system for managing a mortgage-backed securities indexaccording to claim 22, wherein said threshold value is 0.4% for all15-year mortgage-backed securities pools.
 25. A system for managing amortgage-backed securities index according to claim 21 wherein saidrelative weight of said each security within said selected set is givenby the following equation:${w = \frac{\lbrack {x_{c,t}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}},$

wherein w is said relative weight of said each security within saidselected set.
 26. A system for managing a mortgage-backed securitiesindex according to claim 16 wherein said total return means furthercomprises means for calculating said total return of said each securitywithin said selected set.
 27. A system for managing a mortgage-backedsecurities index according to claim 26 wherein said means forcalculating calculates said total return of said each security withinsaid selected set on any given day t₂ in accordance with the followingequation:${{T\quad R_{t_{2}}^{j}} = \frac{{- p_{t_{1}}} + {f_{t_{1}}p_{t_{2}}} + {\lbrack {( {1 - f_{t_{1}}} ) + \frac{c}{12}} \rbrack \lbrack {1 + {r_{t_{1}}\frac{|d|}{360}}} \rbrack}^{- k}}{p_{t_{1}}}},$

wherein p_(t) ₁ is a same-day settle price of said each security on theclose of day t₁, wherein p_(t) ₂ is a same-day settle price of said eachsecurity on the close of day t₂, wherein r_(t) ₁ is a one-month BBALIBOR on the close of day t₁, wherein f_(t) ₁ is a monthly pay-downfactor of said each security as best determined by day t₁, said monthlypay-down factor f_(t) ₁ being selected from a sequence of monthlypay-down factors f_(i), t₁ is the last business day of the precedingmonth, t₂ is any day of the current month, and wherein$d = \begin{matrix}\{ \begin{matrix}{\quad {{25 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}\quad {each}\quad {security}\quad {is}\quad {issued}\quad {by}\quad {FNMA}}}\quad} \\\quad \\\quad \\{\quad {{15 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}{\quad \quad}{each}{\quad \quad}{security}\quad {is}{\quad \quad}{issued}{\quad \quad}{by}\quad {GNMA}\quad {or}{\quad \quad}{FHLMC}}}}\end{matrix}  \\{and} \\{k = \{ \begin{matrix}{{+ 1},} & {{{if}\quad d} > 0} \\\quad & \quad \\\quad & \quad \\{{- 1},} & {{{if}\quad d} < 0}\end{matrix} }\end{matrix}$


28. A system for managing a mortgage-backed securities index accordingto claim 27, wherein said sequence of monthly pay-down factors is givenby the following equation:${f_{i} = \frac{{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}} - {\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,{i + 1}}}}{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}}},$

wherein ρ_(α,i) is the principal outstanding of pool α as of the firstof month i, and wherein ρ_(α,i+1) is the principal outstanding of pool αas of the first of month i+1.
 29. A system for managing amortgage-backed securities index according to claim 16, wherein saidsame-day settle price is given by the following equation:${p_{t} = {{\frac{{\overset{\sim}{p}}_{t} + {\frac{c}{12}\frac{d_{1}}{30}}}{1 + {r\quad \frac{d_{2}}{360}}}f_{t}} + \frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}}}},$

wherein {tilde over (p)}_(t) is the TBA price of said security 1-monthforward standard PSA settle on the close of business on day t; whereind₁ is the number of days into the month that 1-month forward standardPSA settle occurs; wherein d₂ is the number of days in between thepurchase date and the standard PSA settle date 1-month forward inclusiveof the former and exclusive of the latter; wherein, for FNMAmortgage-backed securities, d₃ is the number of days between thepurchase date and the 25th of the next month; wherein for GNMA or FHLMCmortgage-backed securities, d₃ is the number of days between thepurchase date and the 15th of the next month; and wherein r is aone-month BBA LIBOR on the close of day t.
 30. A system for managing amortgage-backed securities index according to claim 16 wherein saidtotal return of said index from day to in month k to day t₂ in month nis given by the following equation:${{T\quad R}|_{t_{1}}^{t_{2}}} = {{{( {1 + {T\quad R_{k}} - {T\quad R_{t_{1}}}} )\lbrack {\prod\limits_{i = {k + 1}}^{n - 1}( {1 + {T\quad R_{i}}} )} \rbrack}( {1 + {T\quad R_{t_{2}}}} )} - 1}$

when k<n−1, wherein TR_(t) ₁ is the month-to-date total return of saidindex on the day t₁, and TR_(t) ₂ is the moth-to-date total return ofsaid index on the day t₂, wherein TR_(k) is the total return of theindex for the month k, and wherein TR_(i) is the total return of theindex for any intermediate month between k and n.
 31. A system formanaging a mortgage-backed securities index according to claim 30wherein said total return of the index for any intermediate month isgiven by the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i\quad i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein said total returns of said index on the day t₁ and t₂ are givenby the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i}^{j}T\quad R_{t}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein {w_(i)^(j)}_(j = 1)^(n)

are the relative weights of said mortgage-backed securities within saidindex, and wherein p_(i) ^(j) is the same-day settle price for said eachsecurity within said index.
 32. A system for managing a mortgage-backedsecurities index according to claim 16 wherein said total return of saidindex from day t₁ in month k to day t₂ in month n is given by thefollowing equation: TR| _(t) ₁ ^(t) ^(₂) =TR _(t) ₂ −TR _(t) ₁ when k=n,wherein TR_(t) ₁ is the total return of said index on the day t₁, andTR_(t) ₂ is the total return of said index on the day t₂.
 33. A systemfor managing a mortgage-backed securities index according to claim 16wherein said total return of said index from day to in month k to day t₂in month n is given by the following equation: TR| _(t) ₁ ^(t) ^(₂)=(1+TR _(k) −TR _(t) ₁ )(1+TR _(t) ₂ )−1 when k=n−1, wherein TR_(t) ₁ isthe total return of said index on the day t₁, wherein TR_(t) ₂ is thetotal return of said index on the day t₂, and wherein TR_(k) is thetotal return of the index for the month k.
 34. A system for managing amortgage-backed securities index according to claim 16, furthercomprising level means, said level means determining a level of saidmortgage-backed securities index.
 35. A system for managing amortgage-backed securities index according to claim 34 wherein saidlevel is given by the following equation:${\frac{P_{t}}{P_{{00/00}/00}} = {{1 + {TR}}|_{{00/00}/00}^{t}}},$

wherein P_(t) is said level of said mortgage-backed securities index onthe day t, wherein P_(00/00/00) is a starting level of said index, andwherein TR|_(00/00/00) ^(t) is the total return of said index from thestarting date to the day t.
 36. A system for managing a mortgage-backedsecurities index according to claim 35, wherein said starting level ofsaid index is
 100. 37. A system for managing a mortgage-backedsecurities index according to claim 34 further comprising an outputmeans, said output means displaying said level of said mortgage-backedsecurities index and said total return of said mortgage-backedsecurities index to the user.
 38. A mortgage-backed securities index,comprising: a set of mortgage-backed securities, said set ofmortgaged-backed securities being selected from all outstandingmortgage-backed securities: wherein a relative weight is assigned toeach security within said selected set, said relative weight being arelative proportion of total outstanding principal on said each securityto the total outstanding principal on all securities within saidselected set, and wherein said mortgage-backed securities index ischaracterized by a total return of said mortgage-backed securitiesindex, said total return being calculated based on said assignedrelative weight for said each security, and a total return of said eachsecurity based on a same-day-settle price.
 39. A mortgage-backedsecurities index according to claim 38, wherein said selected set ofmortgage-backed securities is selected by aggregating said alloutstanding mortgage-backed securities into a plurality of pools, eachof said pools comprising mortgage-backed securities having the samecoupon and the same original term; and calculating an inclusion criteriafor each pool within said plurality of pools.
 40. A mortgage-backedsecurities index according to claim 39, wherein said inclusion criteriais given by the following equation:$x_{c,t} = \frac{\lbrack {\sum\limits_{a = {\{\begin{matrix}{FNMA} \\{GNMA} \\{FHLMC}\end{matrix}\}}}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}$

wherein ρ_(a,c,t) is the total outstanding principal on said outstandingmortgage-backed securities, a is an agency which issued said outstandingmortgage-backed securities, c is a coupon value of said outstandingmortgage-backed securities, and t is an original term of saidoutstanding mortgage-backed securities.
 41. A mortgage-backed securitiesindex according to claim 40, wherein if said inclusion criteria for aparticular pool is greater than a threshold value, said particular poolis included in said selected set.
 42. A mortgage-backed securities indexaccording to claim 41, wherein said threshold value is 1.5% for all30-year mortgage-backed securities pools.
 43. A mortgage-backedsecurities index according to claim 41, wherein said threshold value is0.4% for all 15-year mortgage-backed securities pools.
 44. Amortgage-backed securities index according to claim 40 wherein saidrelative weight of said each security within said selected set is givenby the following equation:$w = {\frac{\lbrack {x_{c,t}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}.}$


45. A mortgage-backed securities index according to claim 44, whereinsaid total return of said each security within said selected set on anygiven day t₂ is given by the following equation:${{T\quad R_{t_{2}}^{j}} = \frac{{- p_{t_{1}}} + {f_{t_{1}}p_{t_{2}}} + {\lbrack {( {1 - f_{t_{1}}} ) + \frac{c}{12}} \rbrack \lbrack {1 + {r_{t_{1}}\frac{|d|}{360}}} \rbrack}^{- k}}{p_{t_{1}}}},$

wherein p_(t) ₁ is a same-day settle price of said each security on theclose of day t₁, wherein p_(t) ₂ is a same-day settle price of said eachsecurity on the close of day t₂, wherein r_(t) ₁ , is a one-month BBALIBOR on the close of day t₁, wherein f_(t) ₁ is a monthly pay-downfactor of said each security as best determined by day t₁, said monthlypay-down factor f_(t) ₁ being selected from a sequence of monthlypay-down factors f_(i), t₁ is the last business day of the precedingmonth, t₂ is any day of the current month, and wherein $\begin{matrix}{d = \{ \begin{matrix}{\quad {{25 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}\quad {security}\quad {is}\quad {issued}\quad {by}\quad {FNMA}}}\quad} \\\quad \\\quad \\{\quad {{15 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}\quad {security}\quad {is}{\quad \quad}{issued}{\quad \quad}{by}\quad {GNMA}\quad {or}{\quad \quad}{FHLMC}}}}\end{matrix} } \\{and} \\{k = \{ \begin{matrix}{{+ 1},} & {{{if}\quad d} > 0} \\\quad & \quad \\\quad & \quad \\{{- 1},} & {{{if}\quad d} < 0}\end{matrix} }\end{matrix}$


46. A mortgage-backed securities index according to claim 45, whereinsaid sequence of monthly pay-down factors is given by the followingequation:${f_{i} = \frac{{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}} - {\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,{i + 1}}}}{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}}},$

wherein ρ_(α,i) is the principal outstanding of pool α as of the firstof month i, and wherein ρ_(α,i+1) is the principal outstanding of pool αas of the first of month i+1.
 47. A mortgage-backed securities indexaccording to claim 46, wherein said same-day settle price is given bythe following equation:${p_{t} = {{\frac{{\overset{\sim}{p}}_{t} + {\frac{c}{12}\frac{d_{1}}{30}}}{1 + {r\quad \frac{d_{2}}{360}}}f_{t}} + \frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}}}},$

wherein {tilde over (p)}_(t) is the TBA price of said security 1-monthforward standard PSA settle on the close of business on day t; whereind₁ is the number of days into the month that 1-month forward standardPSA settle occurs; wherein d₂ is the number of days in between thepurchase date and the standard PSA settle date 1-month forward inclusiveof the former and exclusive of the latter; wherein, for FNMAmortgage-backed securities, d₃ is the number of days between thepurchase date and the 25th of the next month; wherein for GNMA or FHLMCmortgage-backed securities, d₃ is the number of days between thepurchase date and the 15th of the next month; and wherein r is aone-month BBA LIBOR on the close of day t.
 48. A mortgage-backedsecurities index according to claim 47, wherein said total return ofsaid index from day t₁ in month k to day t₂ in month n is given by thefollowing equation:${{{T\quad R}|_{t_{1}}^{t_{2}}} = {{{( {1 + {T\quad R_{k}} - {T\quad R_{t_{1}}}} )\lbrack {\prod\limits_{i = {k + 1}}^{n - 1}( {1 + {T\quad R_{i}}} )} \rbrack}( {1 + {T\quad R_{t_{2}}}} )} - 1}},$

wherein TR_(t) ₁ is the month-to-date total return of said index on theday t₁, and TR_(t) ₂ is the moth-to-date total return of said index onthe day t₂, wherein TR_(k) is the total return of the index for themonth k, and wherein TR_(i) is the total return of the Index for anyintermediate month between k and n.
 49. A mortgage-backed securitiesindex according to claim 48 wherein said total return of the index forany intermediate month is given by the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i\quad i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein said total returns of said index on the day t₁ and t₂ are givenby the following equation${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i}^{j}T\quad R_{t}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein {w_(i)^(j)}_(j = 1)^(n)

are the relative weights of said mortgage-backed securities within saidindex, and wherein p_(i) ^(j) is the same-day settle price for said eachsecurity within said index.
 50. A mortgage-backed securities indexaccording to claim 49, wherein said index is further characterized by alevel, said level being given by the following equation:${\frac{P_{t}}{P_{{00/00}/00}} = {{1 + {TR}}|_{{00/00}/00}^{t}}},$

wherein P_(00/00/00) is the starting level of said index, whereinTR|_(00/00/00) ^(t) is the total return of said index from start to theday t, and wherein P_(t) is the current level of the index.
 51. Amortgage-backed securities index according to claim 50, wherein saidstarting level of said index is
 100. 52. A mortgage-backed securitiesindex according to claim 38, wherein said index is rebalanced by ofselecting a new set of mortgage-backed securities to be included in saidmortgage-backed securities index, assigning said relative weight to eachsecurity within said new selected set, and calculating a new totalreturn of said mortgage-backed securities index.
 53. A mortgage-backedsecurities index according to claim 52 wherein said index is rebalancedon a last business day of each month.
 54. A computer program formanaging a mortgage-backed securities index executable on generalpurpose computer, comprising: an input segment for inputting market datainto said system, said market data comprising data for all outstandingmortgage-backed securities; a selection segment for selecting a set ofmortgage-backed securities to be included in said mortgage-backedsecurities index, said set of mortgaged-backed securities being selectedfrom said all outstanding mortgage-backed securities; a weight segmentfor assigning a relative weight to each security within said selectedset, said relative weight being a relative proportion of totaloutstanding principal on said each security to a total outstandingprincipal on all securities within said selected set; and a total returnsegment for calculating a total return of said mortgage-backedsecurities index, said total return being calculated based on saidassigned relative weight of said each security within said selected set,and a total return of said each security within said selected set basedon a same-day-settle price.
 55. A computer program for managing amortgage-backed securities index according to claim 54 furthercomprising a storage segment, said storage segment storing datacirculated within said system.
 56. A computer program for managing amortgage-backed securities index according to claim 54 furthercomprising a classification segment, said classification segmentclassifying said data for all outstanding mortgage-backed securities inaccordance with a coupon value, issuing agency and original term of eachof said outstanding mortgage-backed securities.
 57. A computer programfor managing a mortgage-backed securities index according to claim 56further comprising an aggregation segment, said aggregation segmentaggregating said outstanding mortgage-backed securities into a pluralityof aggregated pools.
 58. A computer program for managing amortgage-backed securities index according to claim 57 wherein saidselection segment further comprises a segment for calculating aninclusion criterion for each of said aggregated pools.
 59. A computerprogram for managing a mortgage-backed securities index according toclaim 58 wherein said inclusion criterion is given by the followingequation:$X_{c,t} = \frac{\lbrack {\sum\limits_{a = {\{\begin{matrix}{FNMA} \\{GNMA} \\{FHLMC}\end{matrix}\}}}\rho_{a,c,t}} \rbrack}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}$

wherein ρ_(a,c,t) is the total outstanding principal on said outstandingmortgage-backed securities, a is an agency which issued said outstandingmortgage-blacked securities, c is a coupon value of said outstandingmortgage-backed securities, and t is an original term of saidoutstanding mortgage-backed securities.
 60. A computer program formanaging a mortgage-backed securities index according to claim 59,further comprising a segment for comparing said inclusion criterion forall of said aggregated pools to a threshold value, and including anaggregated pool in said selected set if said threshold is met.
 61. Acomputer program for managing a mortgage-backed securities indexaccording to claim 60, wherein said threshold value is 1.5% for all30-year mortgage-backed securities pools.
 62. A computer program formanaging a mortgage-backed securities index according to claim 60,wherein said threshold value is 0.4% for all 1.5-year mortgage-backedsecurities pools.
 63. A computer program for managing a mortgage-backedsecurities index according to claim 59 wherein said relative weight ofsaid each security within said selected set is given by the followingequation:$w = \frac{\lfloor {x_{c,t}\rho_{a,c,t}} \rfloor}{\lbrack {\sum\limits_{\underset{\underset{{t = 180},360}{c \in Z}}{{a = {FNMA}},{GNMA},{FHLMC}}}\rho_{a,c,t}} \rbrack}$

wherein w is said relative weight of said each security within saidselected set.
 64. A computer program for managing a mortgage-backedsecurities index according to claim 54 wherein said total return segmentfurther comprises segment for calculating said total return of said eachsecurity within said selected set.
 65. A computer program for managing amortgage-backed securities index according to claim 64 wherein saidsegment for calculating calculates said total return of said eachsecurity within said selected set on any given day t₂ in accordance withthe following equation:${{T\quad R_{t_{2}}^{j}} = \frac{{- p_{t_{1}}} + {f_{t_{1}}p_{t_{2}}} + {\lbrack {( {1 - f_{t_{1}}} ) + \frac{c}{12}} \rbrack \lbrack {1 + {r_{t_{1}}\frac{|d|}{360}}} \rbrack}^{- k}}{p_{t_{1}}}},$

wherein p_(t) ₁ is a same-day settle price of said each security on theclose of day t₁, wherein p_(t) ₂ is a same-day settle price of said eachsecurity on the close of day t₂, wherein r_(t) ₁ is a one-month BBALIBOR on the close of day t₁, wherein f_(t) ₁ is a monthly pay-downfactor of said each security as best determined by day t₁, said monthlypay-down factor f_(t) ₁ being selected from a sequence of monthlypay-down factors f_(i), t₁ is the last business day of the precedingmonth, t₂ is any day of the current month, and wherein$d = \begin{matrix}\{ \begin{matrix}{\quad {{25 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}\quad {each}\quad {security}\quad {is}\quad {issued}\quad {by}\quad {FNMA}}}\quad} \\\quad \\\quad \\{\quad {{15 - {{day}\quad {of}\quad {the}\quad {month}\quad {of}\quad t_{2}}},{{if}\quad {said}{\quad \quad}{each}{\quad \quad}{security}\quad {is}{\quad \quad}{issued}{\quad \quad}{by}\quad {GNMA}\quad {or}{\quad \quad}{FHLMC}}}}\end{matrix}  \\{and} \\{k = \{ \begin{matrix}{{+ 1},} & {{{if}\quad d} > 0} \\\quad & \quad \\\quad & \quad \\{{- 1},} & {{{if}\quad d} < 0}\end{matrix} }\end{matrix}$


66. A computer program for managing a mortgage-backed securities indexaccording to claim 65, wherein said sequence of monthly pay-down factorsis given by the following equation:${f_{i} = \frac{{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}} - {\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,{i + 1}}}}{\sum\limits_{{\alpha \quad o} \in A}\rho_{\alpha,i}}},$

wherein ρ_(α,i) is the principal outstanding of pool α as of the firstof month i, and wherein ρ_(α,i+1) is the principal outstanding of pool αas of the first of month i+1.
 67. A computer program for managing amortgage-backed securities index according to claim 54, wherein saidsame-day settle price is given by the following equation:${p_{t} = {{\frac{{\overset{\sim}{p}}_{t} + {\frac{c}{12}\frac{d_{1}}{30}}}{1 + {r\quad \frac{d_{2}}{360}}}f_{t}} + \frac{( {1 - f_{t}} ) + \frac{c}{12}}{1 + {r\quad \frac{d_{3}}{360}}}}},$

wherein {tilde over (p)}_(t) is the TBA price of said security 1-monthforward standard PSA settle on the close of business on day t; whereind₁ is the number of days into the month that 1-month forward standardPSA settle occurs; wherein d₂ is the number of days in between thepurchase date and the standard PSA settle date 1-month forward inclusiveof the former and exclusive of the latter; wherein, for FNMAmortgage-backed securities, d₃ is the number of days between thepurchase date and the 25th of the next month; wherein for GNMA or FHLMCmortgage-backed securities, d₃ is the number of days between thepurchase date and the 15th of the next month; and wherein r is aone-month BBA LIBOR on the close of day t.
 68. A computer program formanaging a mortgage-backed securities index according to claim 54wherein said total return of said index from day t₁ in month k to day t₂in month n is given by the following equation:${{T\quad R}|_{t_{1}}^{t_{2}}} = {{{( {1 + {T\quad R_{k}} - {T\quad R_{t_{1}}}} )\lbrack {\prod\limits_{i = {k + 1}}^{n - 1}( {1 + {T\quad R_{i}}} )} \rbrack}( {1 + {T\quad R_{t_{2}}}} )} - 1}$

when k<n−1, wherein TR_(t) ₁ is the month-to-date total return of saidindex on the day t₁, and TR_(t) ₂ is the moth-to-date total return ofsaid index on the day t₂, wherein TR_(k) is the total return of theIndex for the month k, and wherein TR_(i) is the total return of theindex for any intermediate month between k and n.
 69. A computer programfor managing a mortgage-backed securities index according to claim 68,wherein said total return of the index for any intermediate month isgiven by the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i\quad i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein said total returns of said index on the day t₁ and t₂ are givenby the following equation:${{T\quad R_{i}} = \frac{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{i}^{j}T\quad R_{i}^{j}}}{\sum\limits_{j = 1}^{n}{w_{i}^{j}p_{\quad i}^{j}}}},$

wherein {w_(i)^(j)}_(j = 1)^(n)

are the relative weights of said mortgage-backed securities within saidindex, and wherein p_(i) ^(j) is the same-day settle price for said eachsecurity within said index.
 70. A computer program for managing amortgage-backed securities index according to claim 54 wherein saidtotal return of said index from day t₁ in month k to day t₂ in month nis given by the following equation: TR| _(t) ₁ ^(t) ^(₂) =TR _(t) ₂ −TR_(t) ₁ when k=n, wherein TR_(t) ₁ is the total return of said index onthe day t₁, and TR_(t) ₂ is the total return of said index on the dayt₂.
 71. A computer program for managing a mortgage-backed securitiesindex according to claim 54 wherein said total return of said index fromday t₁ in month k to day t₂ in month n is given by the followingequation: TR| _(t) ₁ ^(t) ^(₂) =(1+TR _(k) −TR _(t) ₁ )(1+TR _(t) ₂ )−1when k=n−1, wherein TR_(t) ₁ is the total return of said index on theday t₁, wherein TR_(t) ₂ is the total return of said index on the day t₂and wherein TR_(k) is the total return of the index for the month k. 72.A computer program for managing a mortgage-backed securities indexaccording to claim 54, further comprising level segment, said levelsegment determining a level of said mortgage-backed securities index.73. A computer program for managing a mortgage-backed securities indexaccording to claim 72 wherein said level is give n by the followingequation:${\frac{P_{t}}{P_{{00/00}/00}} = {{1 + {TR}}|_{{00/00}/00}^{t}}},$

wherein P_(t) is said level of said mortgage-backed securities index onthe day t, wherein P_(00/00/00) is a starting level of said index, andwherein TR|_(00/00/00) ^(t) is the total return of said index from thestarting date to the day t.
 74. A computer program for managing amortgage-backed securities index according to claim 73, wherein saidstarting level of said index is
 100. 75. A computer program for managinga mortgage-backed securities index according to claim 72 furthercomprising an output segment, said output segment displaying said levelof said mortgage-backed securities index and said total return of saidmortgage-backed securities index to the user.